Quantum Speedup of Natural Gradient for Variational Bayes
This work addresses a bottleneck in variational Bayes for machine learning practitioners, offering a potential quantum speedup, though it appears incremental as it builds on existing quantum matrix inversion techniques.
The authors tackled the computational expense of natural gradient estimation in variational Bayes by proposing a regression-based method with convergence guarantees, enabling quantum matrix inversion to speed up VB for a broad range of models without requiring simplified distributions.
Variational Bayes (VB) is a critical method in machine learning and statistics, underpinning the recent success of Bayesian deep learning. The natural gradient is an essential component of efficient VB estimation, but it is prohibitively computationally expensive in high dimensions. We propose a computationally efficient regression-based method for natural gradient estimation, with convergence guarantees under standard assumptions. The method enables the use of quantum matrix inversion to further speed up VB. We demonstrate that the problem setup fulfills the conditions required for quantum matrix inversion to deliver computational efficiency. The method works with a broad range of statistical models and does not require special-purpose or simplified variational distributions.